An Adaptive Core-Nash Bargaining Game Consensus Mechanism for Group Decision Making

As a process for ensuring the agreeable degree of individual opinions, consensus analysis is crucial for GDM. This paper focuses on the adaptive consensus mechanism. That's, different adjustment strategies are employed for various consensus levels. Unlike the feedback iteration method, this paper introduces an optimization model-based consensus-reaching procedure. To do this, optimal models are built to determine the minimum consensus adjustment at different levels. Then, the individual minimum consensus adjustment is analyzed, and the inconsistency between individual and group minimum consensus adjustments is concluded. After that, consensus adjustment cooperative games at three levels are proposed to allocate the total minimum consensus adjustment in view of the comprehensive evaluation. We can obtain the coalitional stability allocation scheme using the core of constructed cooperative games. Additionally, core-Nash bargaining games at three levels are proposed to ensure the fairness and coalitional stability of allocation results. Finally, a numerical example is offered to indicate the application of the new theoretical developments.